# Delta(U) = Cvdelta(T) for Ideal Gases?

• Lairix
Bhagat: "In summary, the lecture explains that the internal energy of an ideal gas is a function only of temperature, which is demonstrated through a thought experiment with a real gas. This is why Delta(U) = Cvdelta(T) is always true for Ideal Gases, even in processes where the gas is expanding or being compressed."
Lairix
I don't understand how Delta(U) = Cvdelta(T) is always true for Ideal Gases...Shouldn't this only be true for constant volume processes? Yet it seems to be used even when a gas is expanding or being compressed...

Lairix said:
I don't understand how Delta(U) = Cvdelta(T) is always true for Ideal Gases...Shouldn't this only be true for constant volume processes? Yet it seems to be used even when a gas is expanding or being compressed...

The internal energy of an ideal gas is a function only of temperature. We know this because, if you have a real gas at low pressure in half of a rigid container and vacuum in the other half, and you break the seal, after the system has re-equilibrated at a lower pressure, the temperature does not change. This shows that the internal energy does not depend on pressure. A real gas in the limit of low pressures is what we refer to as an ideal gas.

Chet

## What is the equation for the change in internal energy for ideal gases?

The equation for the change in internal energy (ΔU) for ideal gases is ΔU = CvΔT, where Cv is the heat capacity at constant volume and ΔT is the change in temperature.

## What does the symbol "Cv" represent in the equation?

The symbol "Cv" represents the heat capacity at constant volume, which is the amount of heat required to raise the temperature of a substance by one degree while keeping its volume constant.

## Can this equation be used for non-ideal gases?

No, this equation only applies to ideal gases, which are hypothetical gases that follow the ideal gas law under all conditions.

## How is this equation derived?

This equation is derived from the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system. For ideal gases, the work done is zero, so the change in internal energy is equal to the heat added, which is represented by CvΔT.

## What are the units for Cv and ΔT in this equation?

The units for Cv depend on the units used for temperature and energy, but they are typically in joules per mole per Kelvin (J/molK). The units for ΔT are in Kelvin (K).

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